78
Voted
DM
2008
15 years 23 days ago
2008
We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algor...
81
Voted
DM
2008
15 years 23 days ago
2008
A (d, d + 1)-graph is a graph whose vertices all have degrees in the set {d, d + 1}. Such a graph is semiregular. An (r, r + 1)-factorization of a graph G is a decomposition of G ...
82
Voted
DM
2008
15 years 23 days ago
2008
It is proved that edges of a graph G with no component K2 can be coloured using at most 2 log2 (G) + 1 colours so that any two adjacent vertices have distinct sets of colours of t...
62
Voted
DM
2008
15 years 23 days ago
2008
70
Voted
DM
2008
15 years 23 days ago
2008
106
Voted
DM
2008
15 years 23 days ago
2008
Ore presented a degree condition involving every pair of nonadjacent vertices for a graph to be hamiltonian. Fan (J. Combin. Theory Ser. B 37 (1984) 221
94
Voted
DM
2008
15 years 23 days ago
2008
We give new examples of graphs with the n-e.c. adjacency property. Few explicit families of n-e.c. graphs are known, despite the fact that almost all finite graphs are n-e.c. Our ...